research papers

948 doi:10.1107/S205252061402126X Acta Cryst. (2014). B70, 948–962

Acta Crystallographica Section B

Structural Science,Crystal Engineeringand Materials

ISSN 2052-5206

Structure, hydrogen bonding and thermal expansionof ammonium carbonate monohydrate

A. Dominic Fortes,a,b* Ian G.

Wood,b Dario Alfe,b Eduardo R.

Hernandez,c Matthias J.

Gutmannd and Hazel A. Sparkese

aDepartment of Earth and Planetary Sciences,

Birbeck, University of London, Malet Street,

London WC1E 7HX, England, bDepartment of

Earth Sciences, University College London,

Gower Street, London WC1E 6BT, England,cInstituto de Ciencia de Materiales de Madrid,

Campus de Cantoblanco, 28049 Madrid, Spain,dISIS Facility, Rutherford Appleton Laboratory,

Harwell Science and Innovation Campus,

Didcot, Oxfordshire OX11 0QX, England, andeSchool of Chemisty, University of Bristol,

Bristol BS8 1TS, England

Correspondence e-mail:

andrew.fortes@ucl.ac.uk

We have determined the crystal structure of ammonium

carbonate monohydrate, (NH4)2CO3�H2O, using Laue single-

crystal diffraction methods with pulsed neutron radiation. The

crystal is orthorhombic, space group Pnma (Z = 4), with unit-

cell dimensions a = 12.047 (3), b = 4.453 (1), c = 11.023 (3) A

and V = 591.3 (3) A3 [�calc = 1281.8 (7) kg m�3] at 10 K. The

single-crystal data collected at 10 and 100 K are comple-

mented by X-ray powder diffraction data measured from 245

to 273 K, Raman spectra measured from 80 to 263 K and an

athermal zero-pressure calculation of the electronic structure

and phonon spectrum carried out using density functional

theory (DFT). We find no evidence of a phase transition

between 10 and 273 K; above 273 K, however, the title

compound transforms first to ammonium sesquicarbonate

monohydrate and subsequently to ammonium bicarbonate.

The crystallographic and spectroscopic data and the calcula-

tions reveal a quite strongly hydrogen-bonded structure

(EHB ’ 30–40 kJ mol�1), on the basis of H� � �O bond lengths

and the topology of the electron density at the bond critical

points, in which there is no free rotation of the ammonium

cation at any temperature. The barrier to free rotation of the

ammonium ions is estimated from the observed librational

frequency to be � 36 kJ mol�1. The c-axis exhibits negative

thermal expansion, but the thermal expansion behaviour of

the a and b axes is ormal.

Received 1 August 2014

Accepted 24 September 2014

1. Introduction

Interactions between the most simple of molecules are of

fundamental interest across diverse areas of the physical

sciences, as well as underpinning a number of important

industrial and biological processes; the ternary system H2O–

CO2–NH3 is no exception. As shown in Fig. 1, many different

solid phases crystallize in this system, including a number of

ternary compounds, these being ammonium carbonate

monohydrate [(NH4)2CO3�H2O], ammonium sesquicarbonate

monohydrate [(NH4)4(H2(CO3)3�H2O] and ammonium bicar-

bonate [(NH4)2HCO3]. Since the earliest contribution to our

knowledge of these materials (e.g. Davy, 1800) there have

been numerous contradictory observations regarding both the

correct composition of the solid phases (cf. Divers, 1870) and

accurate solid–liquid phase equilibria (Terres & Weiser, 1921;

Terres & Behrens, 1928; Janecke, 1929; Guyer et al., 1940;

Guyer & Piechowiez, 1944, 1945; Verbrugge, 1979; Kargel,

1992), in part due to a tendency for mixtures of phases to

crystallize, for equilibrium to be slow to achieve and the

instability of the ‘normal’ ammonium carbonate in air. Indeed

the composition of commercially available ammonium

carbonate has been questioned in the scientific literature up

until relatively recently (Sclar & Carrison, 1963; Kuhn et al.,

2007); a sample of ‘ammonium carbonate’ we purchased from

Sigma-Aldrich (207861, ACS reagent, � 30.0% NH3 basis)

and stored at room temperature proved to consist principally

of ammonium carbamate (NH4�NH2CO2). It is therefore

curious that there has been so little interest in the structure

and properties of these comparatively innocuous materials,

considering the extensive crystallographic studies of related

compounds that are either toxic (ammonium oxalate) or

explosive (ammonium chlorate and ammonium nitrate). The

structure of ammonium sesquicarbonate monohydrate was

reported for the first time just over 10 years ago (Margraf et

al., 2003), whilst the last paper of any significance on the

crystallography of ammonium carbonate mononhydrate was

published 140 years ago (Divers, 1870); the first determination

of its structure and properties form the basis of this work.

Of the compounds shown in Fig. 1, only ammonium bicar-

bonate is known to occur naturally on Earth, as the mineral

teschemacherite. This substance is found in layers of guano in

South Africa and South America (Teschemacher, 1846: Ulex,

1848: Phipson, 1863) and in geothermal waters from New

Zealand (Browne, 1972). It is possible that ammonium

carbonate monohydrate can also occur in the faecal deposits

of marine birds in periglacial environments but has hitherto

eluded discovery by virtue, amongst other things, of being

unstable in air above 273 K.

Ammonium carbonate is more likely to occur as an abun-

dant mineral outside the Earth. Carbon dioxide, ammonia and

water are common in interstellar, cometary and planetary ices

(Allamandola et al., 1999; Mumma & Charnley, 2011; Clark et

al., 2013) and models have indicated that condensation of ice

and ammonium carbonate should have occurred in the

primitive solar nebula (Lewis & Prinn, 1980). Interaction of

CO2 with aqueous ammonia during the accretion or differ-

entiation of icy planetary bodies is likely to have sequestered

any free ammonia in the form of solid ammonium carbonates

(Kargel, 1992), and this is the leading hypothesis for the lack

of any appreciable ammonia or ammonia hydrates on plane-

tary surfaces. It is plausible, therefore, that ammonium

carbonates are major ‘rock-forming’ minerals in the outer

solar system. This has prompted interest in extending current

Pitzer potential models to accommodate likely phase assem-

blages produced by freezing of aqueous ammonia- and

ammonium-bearing liquids in the outer solar system (Marion

et al., 2012), such as may occur in subsurface seas and global

oceans inside Saturn’s moons Enceladus and Titan. In the

same context, ammonium carbonates may have some astro-

biological relevance. Being relatively refractory (and thus

stable) compared with other solar system ices, ammonium

carbonates represent a potentially important reservoir of C, H,

O and N that may be processed by energetic phenomena into

pre-biotic molecules. For example, radiolysis of ammonium

carbonate has been demonstrated to produce simple amino

acids (Hartman et al., 1993). Conversely, ammonium carbo-

nate may be synthesized in situ on the surface of Saturn’s giant

satellite Titan. It is known from laboratory analogue experi-

ments that the organic molecules produced photochemically

in Titan’s dense N2/CH4 atmosphere may be hydrolyzed in

aqueous ammonia to form both urea and amino acids (Poch et

al., 2012). Further hydrolysis of urea would be expected to

form ammonium carbonates (Clark et al., 1933); on Earth, this

process is mediated in soils with the aid of bacterial urease,

whereafter the carbonate breaks down to ammonia and water

(e.g. Chin & Kroontje, 1963). On Titan, meteorite impacts into

the icy bedrock would provide the requisite liquid in the form

of impact melt to hydrolyse any solid organics (Artemieva &

Lunine, 2003, 2005) and both urea and ammonium carbonate

may be substantial by-products, persisting on geological

timescales at the surface temperature of 95 K.

As part of a long-term program of studying planetary

ices, we are investigating the interaction of both reduced

carbon and oxidized carbon with other volatiles to produce

non-stoichiometric compounds (such as clathrates) and stoi-

chiometric compounds (such as carbonates). Our aims here

are:

(i) to provide data necessary to identify this material in

planetary environments, whether by in situ X-ray diffracto-

metry (Fortes et al., 2009) or by in situ Raman scattering (e.g.

Jehlicka et al., 2010), and

(ii) to lay the foundations for measuring the thermoelastic

properties necessary to include ammonium carbonate in

structural and evolutionary models of icy planetary body

interiors.

research papers

Acta Cryst. (2014). B70, 948–962 A. Dominic Fortes et al. � Structure of ammonium carbonate monohydrate 949

Figure 1The ternary system H2O–CO2–NH3. With the exception of crystalline endmembers (e.g. water ice, dry ice), the compositions of compounds withknown crystal structures are marked with filled circles; the onlycompound with an as-yet undetermined structure is the title compound,ammonium carbonate monohydrate (marked with an open circle).Numbers indicate the following phases: (1) ammonia dihydrate; (2)ammonia monohydrate; (3) ammonia hemihydrate; (4) ammoniumcarbamate (� and � polymorphs); (5) urea; (6) CO2 clathrate hydrate;(7) solid carbonic acid (� and � polymorphs); (8) ammonium carbonatemonohydrate; (9) ammonium sesquicarbonate monohydrate; (10)ammonium bicarbonate.

2. Experimental and computational methods

2.1. Sample preparation, X-ray powder diffraction andindexing

Crystals were grown by exposing a beaker filled with

aqueous ammonia (Sigma-Aldrich 320145 ACS reagent grade,

28–30% NH3) to a CO2-rich atmosphere inside a loosely

sealed plastic bag charged with dry-ice pellets. Crystals up to

several centimetres in length grew rapidly, their morphology

(Fig. 2) closely resembling that described by Divers (1870).

The distinct herringbone pattern and hollowed-out termi-

nating faces remarked upon by Divers are apparent in our

crystals. We established by X-ray diffraction methods that the

broad face marked ‘2’ in Fig. 2(a) is the (0 1 0) pinacoid. Visual

inspection of our microphotographs leads us to conclude that

faces 3, 4 and 5 in Fig. 2(a) represent the orthorhombic prism

form {2 1 0}, whilst faces 6 and 7 represent the {1 1 2} bipyr-

amid. Both {1 0 0} and {1 0 2} forms occur but we have not

made a detailed morphological or goniometric study. For

comparison, a morphological analysis of ammonium sesqui-

carbonate and bicarbonate crystals is provided by Sainte-

Claire Deville (1854).

Since the crystals readily lose ammonia at room tempera-

ture, all handling and characterization was carried out at low

temperatures in UCL Earth Science’s Cold Room suite (air

temperatures 263–253 K). The large prismatic crystals were

easily extracted from the growth solvent and dried on filter

paper. The initial identification of these crystals was carried

out using X-ray powder diffraction methods, for which

purpose the crystals were ground to a powder in a stainless-

steel pestle and mortar under liquid nitrogen. The measure-

ments were performed on our custom-made portable cold

stage (Wood et al., 2012); this device was pre-chilled in a chest

freezer at 250 K before being loaded. The stage’s Peltier

cooling device was connected to a power supply in the X-ray

diffractometer enclosure within 30 s of leaving the cold room,

ensuring that the specimen did not warm substantially above

253 K prior to the start of the measurement.

X-ray powder diffraction data were acquired on the cold

stage at 245 K using a PANalytical X’Pert Pro diffractometer

with Ge monochromated Co K�1 radiation (� = 1.789001 A).

Comparatively weak Bragg peaks from water ice were iden-

tified, probably due to frozen mother liquor occluded within

the crystals; however, the remaining peaks did not match any

of the other possible known phases in the H2O–CO2–NH3

ternary system and no other match was found in the ICDD by

the proprietary PANalytical ‘High-Score’ software. It is worth

noting that the ICDD pattern described as ‘(NH4)2CO3�H2O’

with peak positions tabulated by Hanawalt et al. (1938; pattern

no. 31), which was presumably measured at room temperature,

was suggested to be a double salt of ammonium carbamate

and ammonium bicarbonate by Sclar & Carrison (1963). A

successful indexing of our unidentified peaks was achieved

using DICVOL06 (Boultif & Louer, 2004), which yielded an

orthorhombic unit cell of dimensions a = 12.129 (3), b =

4.480 (2), c = 10.998 (3) A and V = 597.6 A3 at 245 K. Analysis

of the systematic absences in the diffraction pattern

constrained the space group to one of two possibilities, Pnma

or Pn21a.

Additional X-ray powder diffraction data were collected at

273 and 291 K by reducing the power supplied to the cold

stage. One last aliquot of ammonium carbonate monohydrate

crystals was crushed and allowed to sit in air at 299 K for 2 h;

this material was powdered and then loaded into a standard

spinner sample holder for X-ray powder diffraction analysis

under air at room temperature. Powder diffraction data were

analysed using the GSAS/Expgui package (Larsen & Von

Dreele, 2000: Toby, 2001).

2.2. Neutron single-crystal diffraction and structure solution

A single crystal of the title compound was cut into two

crude cuboids in the UCL Earth Sciences cold room, one

approximately 4 � 4 � 4 mm and the other roughly half the

size. The crystals demonstrated an unfortunate propensity to

cleave parallel to their well developed (0 1 0) faces whilst

being cut. These two crystals were loaded together into a

vanadium tube of 6 mm internal bore and transported to the

ISIS neutron facility under liquid nitrogen. The sample

research papers

950 A. Dominic Fortes et al. � Structure of ammonium carbonate monohydrate Acta Cryst. (2014). B70, 948–962

Figure 2(a) Drawing of ammonium carbonate monohydrate crystal from Divers(1870) compared with photographs of our crystals (b) immersed insolution, and (c) in air.

canister was screwed to the end of a

centre stick whilst being kept

immersed in liquid nitrogen and was

then transferred directly to a closed-

cycle-refrigerator (equilibrated at

100 K) on the SXD beamline (Keen et

al., 2006). After cooling to 10 K, time-

of-flight (t.o.f.) Laue data were

collected in a series of five orienta-

tions, counting each for � 4.5 h. The

diffraction spots were indexed with

the unit cell obtained at 245 K, after

which the intensities were extracted

using the three-dimensional profile

fitting method implemented in

SXD2001 (Gutmann, 2005).

The crystals were removed from

the beamline in order to measure

another specimen, and subsequently

re-mounted after being stored for 2 d

under L-N2, whereupon a second set

of t.o.f. Laue data were obtained at

100 K; these were collected over five

orientations, counting each for � 3 h.

The 10 K data were used to solve

the structure by direct methods with

SHELX2014 (Sheldrick, 2008;

Gruene et al., 2014). The program

SHELXS was used to locate positive

scattering density peaks corre-

sponding to the non-H atoms in the

structure, and refinement with SHELXL was subsequently

used to identify the residual negative peaks due to hydrogen

(arising from the negative neutron scattering length of 1H).

All atomic coordinates were refined anisotropically to yield

the agreement factors listed in Table 1. The maximum and

minimum peaks in the difference Fourier, �� = Fobs � Fcalc,

may seem rather large in comparison to similar X-ray

diffraction measurements and are better understood by

reference to the ‘observed’ nuclear scattering density map,

Fobs, shown in Fig. 3; the difference maxima have magnitudes

approximately 1% of the full range of scattering densities and

are equivalent to approximately 5% of the scattering density

due to a H atom. Consequently, these ‘large’ residual Fourier

peaks should not be interpreted as missing atoms.

2.3. Raman spectroscopy

Laser stimulated Raman spectra were measured using a

portable B&WTek i-Raman Plus spectrometer equipped with

a 532 nm laser (Pmax = 37 mW at the probe tip) that records

spectra over the range 168–4002 cm�1 with a resolution of

� 3 cm�1. Measurements were carried out on large single

crystals of ammonium carbonate monohydrate in our cold

room using the BC100 fibre-optic coupled Raman probe.

Background noise was minimized by acquisition of multiple

integrations, each of 30 to 50 s (at 50% laser power, 18 mW),

the time per integration being limited by detector saturation.

At 263 K spectra were integrated for a total of 600 s.

Measurements made with the crystal at dry ice temperatures

(195 K) or at liquid nitrogen temperatures (77 K) were inte-

grated for 500 and 100 s, respectively.

2.4. Computational methods

In order to confirm the veracity of our structure solution,

and to aid in interpretation of the Raman spectrum, we carried

out a first-principles calculation using density functional

theory (DFT; Hohenberg & Kohn, 1964; Kohn & Sham, 1965),

as implemented in the Vienna Ab initio Simulation Package,

VASP (Kresse & Furthmuller, 1996). The plane-wave expan-

sion was treated using the projected augmented-wave method,

PAW (Blochl, 1994); with the PAW potentials generated by

Kresse & Joubert (1999) and distributed with VASP. The

exchange-correlation was accommodated using the PBE

generalized gradient corrected functional (Perdew et al., 1996,

1997). This form of the generalized gradient approximation

(GGA) has been demonstrated to yield results of comparable

accuracy to higher-level quantum chemical methods, such as

MP2 and coupled-cluster methods, in hydrogen-bonded

systems (e.g. Ireta et al., 2004), despite not correctly repre-

senting dispersion forces.

research papers

Acta Cryst. (2014). B70, 948–962 A. Dominic Fortes et al. � Structure of ammonium carbonate monohydrate 951

Table 1Experimental details.

10 K 100 K

Crystal dataChemical formula CO3�H2O�2H4N CO3�H2O�2H4NMr 114.11 114.11Crystal system, space group Orthorhombic, Pnma Orthorhombic, Pnmaa, b, c (A) 12.047 (3), 4.4525 (11), 11.023 (3) 12.056 (3), 4.4519 (11), 11.016 (3)V (A3) 591.3 (3) 591.2 (3)Z 4 4Radiation type Neutron, � = 0.48-7.0 A Neutron, � = 0.48-7.0 A� (mm�1) 0.00 0.00Crystal size (mm) 4.00 � 4.00 � 4.00 4.00 � 4.00 � 4.00

Data collectionDiffractometer SXD SXDAbsorption correction – –No. of measured, independent and

observed [I > 2�(I)] reflections12 888, 2773, 12 888 7209, 1618, 7209

RefinementR[F 2 > 2�(F 2)], wR(F 2), S 0.091, 0.259, 1.08 0.094, 0.266, 1.09R1 0.0742 0.0713R� 0.0621 0.0585No. of reflections 12 888 7209No. of parameters 104 104No. of restraints 0 0��max, ��min (e A�3) 4.02, �5.60 2.09, �2.52Extinction coefficient 0.048 (3) 0.043 (3)

For completeness, we report the Rietveld R-factors on F2 (R and wR, where the weighting, w, is detailed in the CIFs) as wellas the calculated R-factor based on F (R1), after the reflection set is merged for Fourier-map generation, and a measure ofthe signal to noise ratio in the data, R�. Note that, whilst the values of wR are large and might be deemed unacceptable foran X-ray analysis, these are typical of single-crystal neutron refinements on F2. Computer programs: SXD2001 (Gutmann,2005), SHELXS2014 (Gruene et al., 2014), DIAMOND (Putz & Brandenburg, 2006), publCIF (Westrip, 2010).

Convergence tests were carried out to optimize the k-point

sampling of the Brillouin zone within the Monkhorst–Pack

scheme (Monkhorst & Pack, 1976) and the kinetic energy cut-

off of the plane-wave basis set. It was found that a 2 � 5 � 2 k-

point grid combined with a kinetic energy cut-off of 944 eV

yielded a total-energy convergence better than 10�3 eV per

atom and pressure converged better than 0.2 GPa. A struc-

tural relaxation under zero-pressure athermal conditions was

carried out, starting from the experimental crystal structure

obtained at 10 K, in which the ions were allowed to move

according to the calculated Hellman–Feynman forces and the

unit-cell shape was allowed to vary. The relaxation was

stopped when the forces on each atoms were less than

5 � 10�4 eV A�1 and each component of the stress tensor was

smaller than 0.05 GPa. The phonon spectrum was then

computed using the small displacement method as imple-

mented in the PHON code (Alfe, 2009). The construction of

the full force-constant matrix requires knowledge of the force-

field induced by displacing each atoms in the primitive cell in

the three Cartesian directions. Since there are 68 atoms in the

primitive cell, the total number of required displacements for

this system would then be 408 (allowing for both positive and

negative displacements), although this can be reduced to 84 by

exploiting the symmetry elements present in the crystal. We

used displacements of 0.01 A, which are sufficiently small to

obtain phonon frequencies that are converged to better than

0.1%. Since, in this instance, we are interested only in the

normal modes at the Brillouin zone (BZ) centre, all of the

required information could be obtained by computing the

force matrix for the primitive unit cell. However, in order to

check the mechanical stability of the compound we also

computed the force constant matrix using a 2 � 5 � 2 super-

cell, which is large enough to provide fully converged phonon

frequencies in the whole BZ, and we found no imaginary

phonon branches.

The resulting modes at the BZ centre were classified

according to the irreducible species of point group D2h; this

was done using standard group theory techniques with the

help of the program SAM (Kroumova et al., 2003), available at

the Bilbao crystallographic server (Aroyo et al., 2006).

3. Results and discussion

3.1. Description of the structure and bonding

Fig. 4 depicts the asymmetric unit with atoms labelled

according to the scheme employed in all subsequent figures

and tables. In addition to the tabulated data presented here,

we have deposited supplementary CIFs containing all struc-

ture factors (hkl), refinement output (SHELX RES) and

interatomic distances and angles.1 The results of the athermal

research papers

952 A. Dominic Fortes et al. � Structure of ammonium carbonate monohydrate Acta Cryst. (2014). B70, 948–962

Figure 4The asymmetric unit of ammonium carbonate monohydrate with atomicdisplacement ellipsoids determined at 100 K drawn at the 50%probability level. Dashed rods correspond to hydrogen bonds. Super-scripts denote symmetry operations (i) x; 1

2� y; z; (ii) x; 32� y; z. Three-

dimensional structure visualizations created using DIAMOND (Putz &Brandenburg, 2006).

Figure 3(a) Slice through Fobs, a Fourier map computed from the observedstructure factors phased on the refined atomic coordinates. The sliceshows the nuclear scattering density in the ac plane at b = 0.75; positivemaxima correspond to C, N and O atoms, whereas negative minimacorrespond to H atoms. A drawing of the structure in this plane is shownin Fig. 5. (b) Electron density in the same plane as Fig. 3(a) calculated byVASP at zero pressure and temperature. Two-dimensional visualizationscreated using VESTA (Momma & Izumi, 2011).

1 Supporting information for this paper is available from the IUCr electronicarchives (Reference: EB5035).

zero-pressure DFT structural relaxation are in close agree-

ment with the observed structure (see CIF and Table S1 in the

supporting information).

The CO32� anions have trigonal planar symmetry (point

group D3h) within experimental error and lie in planes

perpendicular to the b-axis at y = 0.25 and 0.75. Each of the

carbonate O atoms accepts three hydrogen bonds, one each in

the plane of the anion and two out-of-plane. The in-plane

hydrogen bonds are donated exclusively by neighbouring

ammonium cations, two from the N(1)H4+ unit, which form

chains of NH4+—CO3

2�—NH4+ extending along the a-axis (Figs.

3 and 5), and one from the N(2)H4+ unit. For O1 and O3, the

out-of-plane hydrogen bonds are donated by NH4+ tetrahedra

in adjacent planes, whereas O2 accepts hydrogen bonds from

the water molecule in adjacent planes. The in-plane hydrogen

bonds from N(1)H4+ cations that form the a-axis chains are

significantly shorter (mean = 1.748 A) than the other in- and

out-of-plane hydrogen bonds (mean = 1.809 A). As shown in

Fig. 6, chains in adjacent sheets are related to one another by

the 21 symmetry operation along b, the result being a fully

three-dimensional hydrogen-bonded framework, albeit with a

strongly layered character. Note that the crystals (Fig. 2) are

elongated in the direction of these strongly hydrogen-bonded

chains and the layering is parallel to the broad (0 1 0) faces.

The only substantial difference between the experimental

and computational structures is in the length and linearity of

the hydrogen bonds donated by and accepted by the water

molecule. In the DFT relaxation, the hydrogen bond accepted

from N(2)H4+ is approximately 4.5% shorter and � 5�

straighter than is observed in the experimental data. The

hydrogen bond donated from H2O to the O2 carbonate

oxygen is � 1.8% shorter than we see experimentally; this

bond is already almost perfectly linear in both the computa-

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Acta Cryst. (2014). B70, 948–962 A. Dominic Fortes et al. � Structure of ammonium carbonate monohydrate 953

Figure 6The complete structure of ammonium carbonate monohydrate is builtfrom the chains shown in Fig. 5 arranged into sheets at y = 0.25 (blurred)and y = 0.75 (sharp). Hydrogen bonds (not shown) extend between thesesheets to form a three-dimensional framework. The unit cell in the acplane is marked by the superimposed box with the 21 symmetry axisindicated by a symbol.

Table 3Comparison of bond angles (�) obtained from DFT calculations andsingle-crystal neutron diffraction at 10 and 100 K.

Ab initio (0 K) 10 K 100 K

H1—N1—H1i 108.14 108.0 (5) 107.6 (7)H1—N1—H2 110.75 110.7 (3) 111.0 (4)H1—N1—H3 108.85 109.2 (3) 109.1 (4)H2—N1—H3 109.46 109.0 (5) 108.9 (7)H4—N2—H4i 109.34 109.7 (4) 109.4 (7)H4—N2—H5 108.23 107.9 (3) 108.1 (5)H4—N2—H6 109.85 110.1 (3) 110.1 (5)H5—N2—H6 111.28 111.0 (5) 111.0 (7)Mean H—N—H 109 (1) 109 (1) 109 (1)H7—Ow1—H7ii 106.39 106.2 (6) 105.7 (9)O1—C1—O2 120.21 120.3 (2) 120.2 (3)O1—C1—O3 120.41 120.2 (3) 120.3 (3)O2—C1—O3 119.38 119.5 (2) 119.6 (3)Mean O—C—O 120.0 (5) 120.0 (4) 120.0 (4)

Symmetry codes: (i) x; 32� y; z; (ii) x; 1

2� y; z.

Table 2Comparison of covalent bond lengths (A, uncorrected for thermalmotion) obtained from DFT calculations and single-crystal neutrondiffraction at 10 and 100 K.

Ab initio (0 K) 10 K 100 K

N1—H1 1.0479 1.040 (3) 1.040 (6)N1—H2 1.0577 1.053 (6) 1.053 (8)N1—H3 1.0552 1.045 (5) 1.048 (8)N2—H4 1.0452 1.040 (3) 1.037 (6)N2—H5 1.0566 1.041 (6) 1.043 (8)N2—H6 1.0492 1.043 (6) 1.039 (8)Mean N—H 1.051 (5) 1.043 (5) 1.042 (5)Ow1—H7 0.9906 0.975 (4) 0.972 (6)C1—O1 1.2975 1.287 (3) 1.286 (4)C1—O2 1.2993 1.287 (3) 1.282 (5)C1—O3 1.3008 1.289 (2) 1.288 (4)Mean C—O 1.299 (2) 1.288 (1) 1.285 (3)

Figure 5The chain motif of alternating hydrogen-bonded carbonate and N1ammonium ions parallel to the a-axis. Note that the N2 ammoniumcations ‘decorate’ this chain, donating the sole hydrogen bond to thewater molecule. This viewing direction corresponds to that shown in Figs.3(a) and (b). As in Fig. 4, dashed rods depict hydrogen bonds.

tional and experimental data. Note that the other calculated

hydrogen-bond lengths are just a few tenths of a percent

different from the single-crystal structure refinements, differ-

ences that have little or no statistical significance. See Tables

2–4.

The carbonate ions are entirely unremarkable, having

nearly identical C—O bond lengths to those found by single-

crystal methods in a large number of other inorganic carbo-

nate minerals (Zemann, 1981; Hesse et al., 1983; Chevrier et

al., 1992; Maslen et al., 1995; Giester et al., 2000) and in

ammonium sesquicarbonate mono-

hydrate (Margraf et al., 2003).

By contrast, there are fewer exam-

ples of accurate N—H bond lengths

for ammonium ions in the literature

obtained by single-crystal neutron

diffraction methods. Moreover, these

ions appear to be more susceptible

than the carbonate ion to variations in

bond length depending on the coor-

dination environment (Brown, 1995;

Demaison et al., 2000). Table 5 lists a

number of experimental and compu-

tational values for the N—H (or N—

D) bond length of the ammonium ion

in the gas phase, in clusters and in

crystals (for which we report only

single-crystal neutron diffraction

data).

The equilibrium N—H bond length

for the gas phase NH4+ ion has been

determined spectroscopically to be

1.029 A (Crofton & Oka, 1987), and

many of the crystallographic values

fall around this value; indeed the

mean of all values listed in Table 5 is

1.026 A. One would expect the N—H

contact to increase in length on

formation of hydrogen bonds, and

there is some computational support

for this; Jiang et al. (1999) reported a

small increase in r(N—H) on forma-

tion of hydrogen-bonded clusters with

water, and in our own earlier work

(Fortes et al., 2001) we found that

r(N—H) increased from 1.055 A in

the free ion to 1.063 A in the hydrogen-bonded NH4OH

crystal. Nonetheless, we still see long N—H bonds (> 1.05 A)

even in weakly hydrogen-bonded crystals, such as ammonium

perchlorate (Choi et al., 1974), where the ammonium ions have

a very low energy barrier to free rotation, � 2 kJ mol�1

(Johnson, 1988; Trefler & Wilkinson, 1969; Westrum & Justice,

1969).

A more accurate picture of the covalent N—H bond in the

ammonium ion may be obtained instead by analysis of the

electron density generated by DFT calculations. Fig. 3(b)

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954 A. Dominic Fortes et al. � Structure of ammonium carbonate monohydrate Acta Cryst. (2014). B70, 948–962

Table 5Experimental and computational N—H bond lengths (A) in ammonium ions in a variety ofenvironments; crystallographic values are all sourced from single-crystal neutron diffraction studies.

Where there is more than one symmetry-inequivalent N—H bond the mean bond length (and standarduncertainties) are reported.

Compound Conditions N—H (A) Reference

NH4+ Gas phase 1.02873 0.00002 Crofton & Oka (1987)

ND4+ Gas phase 1.0267 0.0005 Crofton & Oka (1987)

NH4+ DFT (PW91) 1.055 Fortes et al. (2001)

NH4OH DFT (PW91) 1.063 0.013 Fortes et al. (2001)NH4CN DFT (BLYP) I 1.034 Alavi et al. (2004)NH4CN DFT (BLYP) II 1.050 Alavi et al. (2004)ND4(NH3)n clusters (B3LYP/6-31+G*) 1.046 0.002 Wang et al. (2002)ND4(NH3)n clusters (MP2/6-31+G*) 1.043 0.003 Wang et al. (2002)NH4Cl 295 K 1.050 0.005 Kurki-Suonio et al. (1976)NH4Br 296 K 1.046 0.005 Seymour & Pryor (1970)NH4Br 409 K 1.040 0.005 Seymour & Pryor (1970)NH4�C2O4�H2O 274 K 1.029 0.005 Taylor & Sabine (1972)ND4�C2O4�D2O 274 K 1.033 0.002 Taylor & Sabine (1972)(NH4)2C4H4O6 Room-temperature 1.04 0.03 Yadava & Padmanabhan (1976)(NH4)2SO4 (Pnma) Room-temperature 1.069 0.018 Schlemper & Hamilton (1966)(NH4)2SO4 (Pna21) � 180 K 1.050 0.016 Schlemper & Hamilton (1966)(NH4)2BeF4 (Pnma) 200 K 0.989 0.014 Srivastava et al. (1999)(NH4)2BeF4 (Pna21) 163 K 1.005 0.015 Srivastava et al. (1999)(NH4)2BeF4 (Pna21) 20 K 1.018 0.015 Srivastava et al. (1999)NH4ClO4 78 K 0.995 0.010 Choi et al. (1974)NH4ClO4 10 K 1.037 0.014 Choi et al. (1974)ND4NO3 (II) 355 K 0.988 0.002 Lucas et al. (1979)NH4NO3 (III) 298 K 1.035 0.007 Choi & Prask (1982)NH4NO3 (IV) 298 K 0.990 0.004 Choi et al. (1972)ND4NO3 (IV) 298 K 0.972 0.008 Lucas et al. (1979)ND4NO3 (V) 233 K 1.006 0.016 Ahtee et al. (1983)NH4�NH3CH2COOH�SO4 Room-temperature 1.031 0.018 Vilminot et al. (1976)(ND4)2Cu(SO4)2�6D2O 15 K 1.028 0.004 Simmons et al. (1993)(ND4)2Cr(SO4)2�6D2O 4.3 K 1.028 0.002 Figgis et al. (1991)(ND4)2Fe(SO4)2�6D2O 4.3 K 1.025 0.006 Figgis et al. (1989)

(NH4)2CO3�H2O 10 K 1.043 0.005 This work100 K 1.042 0.005DFT (PBE) 1.051 0.005

Table 4Hydrogen-bond lengths (A) and angles (�) determined by single-crystal neutron diffraction at 10 and 100 K, and by DFT calculations.

ab initio (0 K) 10 K 100 KH� � �Y (A) X� � �Y (A) X—H� � �Y (�) H� � �Y (A) X� � �Y (A) X—H� � �Y (�) H� � �Y (A) X� � �Y (A) X—H� � �Y (�)

N1—H1� � �O3 1.7640 2.8027 170.44 1.766 (4) 2.797 (2) 170.6 (4) 1.764 (6) 2.796 (2) 170.7 (6)N1—H2� � �O1 1.7308 2.7819 171.89 1.721 (6) 2.766 (3) 171.1 (5) 1.719 (9) 2.765 (4) 171.5 (7)N1—H3� � �O2 1.7436 2.7935 172.75 1.740 (5) 2.778 (2) 171.6 (6) 1.739 (8) 2.781 (4) 171.8 (8)N2—H4� � �O1 1.8224 2.8604 171.58 1.808 (3) 2.840 (1) 171.7 (4) 1.808 (6) 2.838 (2) 171.8 (6)N2—H5� � �Ow1 1.7255 2.7745 171.32 1.807 (7) 2.831 (3) 167.0 (5) 1.805 (10) 2.830 (5) 166.7 (8)N2—H6� � �O3 1.8130 2.8534 170.68 1.814 (6) 2.847 (3) 170.2 (5) 1.816 (8) 2.846 (4) 170.4 (8)Ow1—H7� � �O2 1.7937 2.7843 178.99 1.813 (4) 2.788 (2) 179.6 (5) 1.816 (6) 2.788 (3) 179.8 (7)

depicts a slice through the crystal in the plane of the N1—H2,

N1—H3, N2—H5 and N2—H6 bonds. The properties of these

bonds are described by the topology of the electron density

according to Bader’s quantum theory of atoms in molecules,

QTAIM (Bader, 1990). Of interest to us are the saddle points

where the gradient in the electron density, r�(r), vanishes;

these are known as bond critical points (BCPs). Important

metrics of the bond strength and character are the electron

density at the BCP, �(rBCP), and the Laplacian of the electron

density at the BCP, r2�(rBCP), which itself represents the

3 � 3 Hessian matrix of second partial derivatives of the

electron density with respect to the coordinates. The eigen-

values of this matrix, �1, �2 and �3 (which sum to r2�) are the

principal axes of ‘curvature’ of the electron density perpen-

dicular to the bond (�1, �2) and along the bond (�3). At the

bond critical points these eigenvalues have different signs,

which may lead (particularly for weak bonds, as we will see

later) to Laplacians with small values and comparatively large

uncertainties. Indeed it has been shown by Espinosa et al.

(1999) that the curvature along the bond, �3, provides the

clearest indicator of bond strength. Nonetheless, the Laplacian

is still a widely reported quantity; a negative Laplacian at the

bond critical point generally corresponds to a concentration of

electron density, which is characteristic of a covalent bond,

whereas ionic bonds and hydrogen bonds have a positive

Laplacian, indicative of a depletion in electron density.

We have used the program AIM-UC (Vega & Almeida,

2014) to compute the properties of the electron density at the

N—H bond critical points in ammonium carbonate mono-

hydrate (Table 6). For comparison we have reproduced some

experimental and computational electron density metrics from

other ammonium compounds, revealing some interesting

differences. Note that the density at the BCP is broadly similar

for all compounds, but the Laplacians range from approxi-

mately �10 e A�5 (NH4F) to

�50 e A�5 (this work). Between the

four literature examples (all with N—

H bond lengths of � 1.030 A), much

of the difference lies in the value of �1

and �2; however, for ammonium

carbonate monohydrate the greatest

difference is in �3, which has a value

of� 10 e A�5, relative to 20–30 e A�5

in the other materials. It is intriguing

that such significant differences in

charge distribution should exist within

otherwise similar ionic entities.

Of the two symmetry-inequivalent

NH4+ cations only the N2 unit bonds

with the water molecule, although this

appears to have little effect on either

the N—H or the H� � �O bond between

the ammonium ion and the water

molecule compared with any other

interatomic contact. The water mole-

cules themselves are, however, some-

what unusual in being trigonally

coordinated rather than tetrahedrally coordinated as one

might expect, accepting just a single hydrogen bond from the

H5 atom. However, this is not unprecedented; a similar

arrangement occurs in a number of inorganic hydrates, such as

ammonia dihydrate (Loveday & Nelmes, 2000; Fortes et al.,

2003).

Following the example outlined above for the ammonium

ion, we can also use the QTAIM methodology to characterize

the hydrogen-bond network that holds together each of the

material’s molecular and ionic building blocks. Based solely on

the H� � �O distances and N—H� � �O angles, it is clear that

ammonium carbonate monohydrate is relatively unusual

amongst ammonium compounds in having quite strong

hydrogen bonds donated by the ammonium ion. The effect of

this on the vibrational frequencies is also quite clear as

described in the following section. As before, we used AIM-

UC to obtain the coordinates and topological properties of the

bond critical points relating to the hydrogen bonds and these

are listed in Table 7. There are well known correlations

between interatomic distances and the electron density

metrics (particularly �3), and our results are in good agree-

ment with previous experimental and computational values

(Espinosa et al., 1999; Tang et al., 2006).

The dissociation energy of the hydrogen bond may be

estimated accurately from vibrational frequencies and with

varying degrees of accuracy from the electron density (cf.

Vener et al., 2012). The total energy density is the sum of the

local kinetic and potential electronic energies, G(r) and V(r),

respectively, at the BCP (Bader & Beddall, 1972)

H rBCP

� �¼ G rBCP

� �þ V rBCP

� �; ð1Þ

where the potential energy is related to the Laplacian of the

electron density via the local form of the virial theorem

(Bader, 1990)

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Acta Cryst. (2014). B70, 948–962 A. Dominic Fortes et al. � Structure of ammonium carbonate monohydrate 955

Table 6Properties of the electron density at the bond critical points in the ammonium ions as determined byDFT calculations.

Electron density, �(r), is reported in e A�3, whereas the Laplacian, r2�(r), and the eigenvalues of theHessian matrix, �1, �2 and �3, are given in e A�5.

Fractional coordinates of BCP Topology of electron density at BCP

x y z �(r) r2�(r) �1 �2 �3

N1—H1 0.1166 0.6071 0.0868 2.1581 �47.083 �29.697 �28.538 11.152N1—H2 0.0344 0.7500 0.1360 2.0971 �45.462 �28.166 �27.760 10.464N1—H3 0.1314 0.7500 0.1859 2.1145 �46.979 �28.915 �28.472 10.407N2—H4 0.1299 0.8928 0.6928 2.1795 �47.348 �30.163 �28.644 11.460N2—H5 0.0672 0.7500 0.6194 2.1038 �48.144 �29.216 �28.682 9.754N2—H6 0.1748 0.7500 0.6052 2.1512 �48.482 �30.035 �29.192 10.744

NH4F† � Expt. 1.975 �13.0 �22.3 �21.6 31.0Calc. 1.865 �11.2 �21.1 �20.2 30.3

NH4HF2† � Expt. 2.230 �35.0 �33.8 �31.3 30.1Calc. 2.185 �28.3 �29.2 �28.9 29.7

NH4�B6H6‡ Calc. 2.220 �34.0 �29.6 �29.3 24.8NH4�C2HO4�C2H2O4�2H2O§ Expt. 2.207 �37.0 �30.1 �29.3 22.4

† van Reeuwijk et al. (2000). ‡ Mebs et al. (2013) – �1 and �2 estimated from the quoted bond ellipticity [" = �1/ �2) � 1]and the Laplacian. § Stash et al. (2013).

V rBCP

� �¼

1

4r

2� rBCP

� �� 2G rBCP

� �ð2Þ

and the kinetic energy is obtained by partitioning of the

electron density (e.g. Abramov, 1997)

G rBCP

� �¼

3

103�2� �2=3

� rBCP

� �5=3þ

1

6r

2� rBCP

� �: ð3Þ

Espinosa et al. (1998) proposed that the hydrogen-bond

energy, EHB, could be obtained simply from the potential

energy density

EHB ¼ 0:5V rBCP

� �; ð4Þ

and this expression continues to be used widely, whereas Mata

et al. (2011) subsequently suggested that a more accurate value

could be found from the kinetic energy density

EHB ¼ 0:429G rBCP

� �: ð5Þ

A subsequent analysis by Vener et al. (2012) found that

equation (4) systematically overestimates EHB compared with

the spectroscopically determined hydrogen-bond energies.

However, the value given by equation (5) appears to yield

reasonably accurate values of EHB. In Table 8 we detail EHB as

calculated using equations (4) and (5). Furthermore, we give a

‘corrected’ value of EHB based on equation (4) and the

tabulated results in Vener et al. (2012)

such that EHB(corrected) = 0.465EHB

+ 16.58. The mean values of EHB in

the right-hand column thus represent

our most accurate determination of

the hydrogen-bond dissociation

energy in this compound.

The arrangement of the ions in

ammonium carbonate monohydrate

differs in a number of important ways

from related structures. As noted

above, the structure consists of chains

of alternating hydrogen-bonded

cations and anions; i.e. the ions are co-

planar in the plane of the carbonate

ion and it is this co-planarity that is

unusual. In the structures of ammo-

nium sesquicarbonate monohydrate

(Margraf et al., 2003) and ammonium

bicarbonate (Pertlik, 1981; Zhang,

1984) the anions are also arranged

into chains (Fig. 7), but these are

hydrogen bonded by water molecules

and/or the O—H moiety of the

bicarbonate ion. Unlike ammonium

carbonate monohydrate, the cations

in these two structures are situated

between the planes of carbonate

anions.

There are comparatively few other

structures with which to form a direct

comparison of the title compound. Of

the alkali metals for which the

ammonium ion most commonly substitutes, Li, Rb and Cs

form poorly soluble carbonates and no hydrates are known

(Dinnebier et al., 2005); potassium is known only to form a

sesquihydrate, K2CO3�3/2H2O (Skakle et al., 2001). Conver-

sely, Na2CO3 is highly soluble in water and can crystallize as a

decahydrate (the mineral natron), a heptahydrate and a

monohydrate (Wu & Brown, 1975).

Due to the much smaller ionic radius of Na+ relative to NH4+

the structure of sodium carbonate monohydrate differs in

some important respects from that of ammonium carbonate

monohydrate. In Na2CO3�H2O (space group Pca21) there are

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956 A. Dominic Fortes et al. � Structure of ammonium carbonate monohydrate Acta Cryst. (2014). B70, 948–962

Table 8Energetic properties of the hydrogen bonds.

The local kinetic energy density, G(r), the local potential energy density, V(r), and the total energy density,H(r), at the bond critical point are all given in atomic units. Conversion factors used: 1 a.u. of �(r) =6.7483 e A�3; 1 a.u. of r2�(r) = 24.099 e A�5; 1 a.u. of energy density = 2625.4729 kJ mol�1. The hydrogenbond energies, EHB, are in units of kJ mol�1.

Derived hydrogen bond energy

G(r) V(r) H(r)EHB

[equation (4)]EHB

(corr)EHB

[equation (5)] EHB mean

H1� � �O3 0.03009 �0.03604 �0.00595 �47.32 �38.58 �33.89 �36.24H2� � �O1 0.03473 �0.04307 �0.00835 �56.55 �42.87 �39.12 �41.00H3� � �O2 0.03273 �0.03989 �0.00716 �52.37 �40.93 �36.87 �38.90H4� � �O1 0.02619 �0.03035 �0.00416 �39.85 �35.11 �29.50 �32.31H5� � �Ow1 0.03524 �0.04380 �0.00856 �57.50 �43.32 �39.69 �41.50H6� � �O3 0.02711 �0.03279 �0.00568 �43.04 �36.59 �30.53 �33.56H7� � �O2 0.02669 �0.03181 �0.00512 �41.75 �36.00 �30.06 �33.03Mean �36.65

Table 7Properties of the electron density at the bond critical points in the hydrogen bonds as determined fromthe DFT calculations.

Electron density, �(r), is reported in e A�3, whereas the Laplacian, r2�(r), and the eigenvalues of theHessian matrix, �1, �2 and �3, are given in e A�5.

Fractional coordinates of BCP Topology of electron density at BCP

x y z �(r) r2�(r) �1 �2 �3

H1� � �O3 0.1429 0.4558 0.0492 0.2767 2.327 �1.613 �1.539 5.478H2� � �O1 �0.0320 0.7500 0.1548 0.3124 2.543 �1.874 �1.825 6.242H3� � �O2 0.1615 0.7500 0.2539 0.2963 2.465 �1.749 �1.707 5.921H4� � �O1 0.1289 0.4531 0.7430 0.2460 2.124 �1.362 �1.317 4.803H5� � �Ow1 0.0034 0.7500 0.5946 0.3158 2.572 �1.933 �1.854 6.360H6� � �O3 0.2333 0.7500 0.5602 0.2625 2.065 �1.508 �1.440 5.013H7� � �O2 0.1504 0.5358 0.3899 0.2561 2.079 �1.464 �1.414 4.957

Figure 7Comparison of the chain motifs occurring in (a) ammonium sesquicarbo-nate monohydrate and (b) ammonium bicarbonate.

perfectly trigonal CO3 anions lying in planes

perpendicular to the crystal’s a-axis at x =

0.25 and 0.75. Where this structure differs

from the ammonium analogue is that

carbonate anions in adjacent sheets lie

directly above one another (rather than

being offset by half a unit cell) to form

closely packed ‘columns’ of CO3 along the

a-axis. The structure also differs in having

both the cations and the water molecule

lying in discrete sheets between the CO3

planes, much like ammonium sesquicarbo-

nate and bicarbonate. The higher-density

packing results in the helical structure

shown in Fig. 8, linked together by water

molecules in distorted tetrahedral coordi-

nation; by comparison, the ammonium

carbonate crystal has simple zigzag chains

linked by trigonally coordinated water

molecules donating almost perfectly linear

hydrogen bonds.

Amongst other possible analogues,

ammonium nitrate and ammonium chlorate

have no known hydrates: ammonium sulfite

occurs as a monohydrate but this structure

is characterized by non-planar (and non-co-

planar) SO3 anions (Battelle & Trueblood,

1965) and so there is little to be gained by

discussing this further. Only two other compounds are of any

possible interest, these being ammonium carbonate peroxide

(Medvedev et al., 2012) and ammonium oxalate monohydrate

(Robertson, 1965; Taylor & Sabine, 1972). In both of these

compounds the (roughly) planar anions are linked in-plane by

water or hydrogen peroxide rather than the ammonium

cations. In summary, there are no obvious structural analogues

amongst any plausible related compounds and the occurrence

of co-planar anions and cations in these types of structures

seems to be uncommon.

3.2. Vibrational spectra

Ammonium carbonate monohydrate crystallizes in the

centrosymmetric space group Pnma having a primitive cell

with D2h point-group symmetry and four formula units per

unit cell; all ions and molecules are located on sites of CS

[�(xz)] symmetry. Based on a consideration of the normal

vibrational modes of the free ammonium and carbonate ions

and the neutral water molecule, we have carried out a factor

group analysis by the correlation method to determine the

symmetry species of all Raman-active modes. Allowing for the

modes corresponding to translation of the entire crystal (2A0 +

A00), we find that there are 102 normal modes summarized as

�opt(Raman) = 31Ag + 20B1g + 31B2g + 20B3g. The DFT-

calculated frequencies of these 102 normal modes are shown

in relation to the observed Raman spectrum in Fig. 9.

The Raman spectrum is dominated by strong symmetric

stretching modes from the carbonate ion (split into a strong Ag

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Acta Cryst. (2014). B70, 948–962 A. Dominic Fortes et al. � Structure of ammonium carbonate monohydrate 957

Figure 8Comparison of the water–carbonate structures formed in (a) ammoniumcarbonate monohydrate and (b) sodium carbonate monohydrate.

Table 9Assignment of observed Raman-active vibrational modes in ammonium carbonate mono-hydrate at 80 K.

Observedfrequency(cm�1)

Relativeintensity(%) Assignment

Observedfrequency(cm�1)

Relativeintensity(%) Assignment

175.2 (4) 3.2 – 1935 (1) 1.9 �NHþ4 ð4 þ librÞ218.5 (1) 42.9 9=

; NHþ4 transl:

1990 (2) 3.4234.1 (1) 26.5 2037 (4) 0.9258.6 (1) 21.9 2185.9 (6) 1.0 9=

; NHþ4 ð2 þ libr:Þ280.9 (1) 16.6 2226.9 (1) 5.9507 (1) 2.0 9=

; NHþ4 libr

2263.1 (2) 3.0528.0 (4) 1.2 2296.5 (5) 1.0573 (2) 0.7 2683.0 (3) 11.1 �

NHþ4 3 in-plane608 (3) 0.4 2774.1 (3) 7.5687.6 (6) 3.0 �

CO2�3 4

2839.8 (3) 9.6709.2 (6) 1.7 2889.5 (2) 36.5 NH4

+ 1

745.3 (5) 3.7 H2O libr 2903 (2) 15.6 �NHþ4 3 out-of-plane966 (5) 1.4 – 2976 (5) 12.4

1056.8 (7) 7.2 CO32� 1(B2g) 3011 (2) 16.0

1074.66 (4) 100.0 CO32� 1(Ag) 3066 (3) 2.1 –

1115 (4) 1.3 – 3094 (1) 10.4 –1384.8 (2) 2.3 CO3

2� 3(Ag) 3134 (2) 3.0 –1424.3 (3) 2.7 CO3

2� 3(B2g) 3224 (1) 2.8 NH4+ (2 + 4)?

1474.9 (2) 3.5 9=; NHþ4 4

3296.88 (4) 43.9 H2O 1/3

1497.8 (1) 5.0 3357 (1) 4.4 �NHþ4 ð22Þ?1517.5 (4) 1.2 3494 (1) 1.8

1555.0 (2) 2.9 – – –1696.4 (5) 2.0 9>>=

>>;NHþ4 2

– – –1727.3 (1) 8.1 – – –1745.2 (2) 2.6 – – –1756.3 (3) 2.9 – – –1769 (1) 0.8 – – –

symmetry peak at 1074 cm�1 and a weaker B2g symmetry peak

at 1056 cm�1), from the ammonium ions (2889 cm�1) and from

the water molecule (3297 cm�1). These are in good agreement

with the calculated frequencies, 1044.5, 1008.3, 2920 (average)

and 3343 (average) cm�1, respectively.

Moderately strong Raman peaks occur in the low-frequency

range, between 218 and 280 cm�1, which are due to transla-

tional motions of the ammonium ions, and in the high-

frequency range (2600–3000 cm�1) due to the asymmetric N—

H stretch of NH4+. The latter are divided into motions in the

crystal’s mirror plane (on the low-frequency side of 1 NH4+)

and motions out of the mirror plane (on the high-frequency

side of 1 NH4+). Amongst these modes, peaks due to the

N(1)H4+ tetrahedron occur at lower frequency than those due

to N(2)H4+, which is likely to reflect the influence of the shorter

(i.e. stronger) hydrogen bonds donated by N(1)H4+ (see, for

example, Tables 4 and 8). Fig. 10 illustrates a deconvolution of

the high-frequency portion of the spectrum into separate

Lorentzian contributions.

In the range 1300–1850 cm�1 (Fig. 11) we observe the

asymmetric stretch of the carbonate ion, split into Ag and B2g

peaks at 1385 and 1424 cm�1, the asymmetric deformation of

the NH4+ ion between 1475 and 1555 cm�1, and the symmetric

deformation of the NH4+ ions (scissor and twist modes) from

around 1696 to 1769 cm�1. The symmetric bending mode of

the water molecule is sometimes observed as a very weak

feature near 1650 cm�1 [2(Ag) at 1637.7 cm�1 and 2(B2g) at

1636.8 cm�1 according to our DFT calculations], but this

seems to be absent in our measured spectra. It is conceivable

that the peak at 1696.1 cm�1 is due to this vibrational mode,

but the arguments concerning combination bands made below

suggest that this is not the case.

Between 300 and 1000 cm�1 there are some weak features,

the first (from � 507 to 608 cm�1) being due to librational

motion of the NH4+ ions. A doublet at 687.6 and 709.2 cm�1 is

attributable to asymmetric bending of the carbonate ion,

whilst the peak at 745 cm�1 is probably due to libration of the

water molecules.

The frequencies of normal modes attributed to the carbo-

nate ion are in excellent agreement with literature data for

numerous other carbonate compounds (e.g. Buzgar & Apopei,

2009). However, the positions of the NH4+ stretching modes

are substantially red-shifted, and those of the bending modes

substantially blue-shifted, from the observed vibrational

frequencies of the free ion and of ammonium in weakly

hydrogen-bonded solids (see Brown, 1995, and references

therein). The pattern of shifts is further evidence of the rela-

tively strong hydrogen bonding of the ammonium ion. Indeed

the observed vibrational frequencies are similar to those

observed in one of most strongly hydrogen-bonded ammo-

nium salts, NH4F (Plumb & Hornig, 1955).

Further observational support for strong hydrogen bonding

of the ammonium ion (in addition to the electron-density

analysis in the previous section) is the occurrence of bands

around 2000 and 2200 cm�1 due to the combination of NH4+

bending modes (2 and 4) with the librational modes (6).

Their presence is strongly supportive of rotational hindrance

caused by hydrogen bonding. Since the strongest NH4+ libra-

tional peak is at 507 cm�1, we have simply red-shifted the

combination bands by a uniform 500 cm�1 in Fig. 12 in order

to compare their structure with the 2 and 4 regions. Note the

occurrence of the 1696 cm�1 peak in the combination bands,

suggesting that it is due to ammonium rather than water.

Finally, the frequency of the ammonium librational mode is

much higher than in many other ammonium salts; using the

empirical relationship of Sato (1965) we use the observed

librational frequency to derive a barrier to free rotation of

36 kJ mol�1. Not only is this large (cf. Johnson, 1988), being

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958 A. Dominic Fortes et al. � Structure of ammonium carbonate monohydrate Acta Cryst. (2014). B70, 948–962

Figure 10Deconvolution of the high-frequency bands and interpretation in terms ofthe normal modes, overtones and combinations responsible. Individualpure Lorentzian contributions are drawn in red whilst the sum is drawn inblue. Band centres are obtained by least-squares fitting. The scatterplotsunderneath the spectrum reports the residuals between the best fit andthe data.

Figure 9Raman spectra of ammonium carbonate monohydrate collected at 263 K(bottom), 195 K (middle) and 80 K (top). DFT-calculated Raman-activezone-centre phonon frequencies of various symmetries (Ag, B1g, B2g andB3g) are shown by vertical tick marks beneath the spectra. Broadidentifications of the normal modes and combinations responsible for theobserved bands are labelled. Additional details are given in Table 9 andFigs. 10–12.

comparable to NH4F (44 kJ mol�1), but it is strikingly similar

to the mean hydrogen-bond energy reported at the bottom of

Table 8.

Inelastic neutron spectra of ‘ammonium carbonate’ were

measured at 293 K by Myers et al. (1967); they determined the

frequencies of the translational and torsional modes as,

respectively, 205 7 and 445 10 cm�1. Whilst it is unlikely

that the material was ammonium carbonate monohydrate in

the form studied by us, their work does note that the

frequency ratio of the two modes for a number of ammonium

salts lies between 1.99 and 2.38, which is in good agreement

with our observations.

3.3. Thermal expansion and decomposition

Since we have collected crystallographic data at several

temperatures (albeit on different instruments using different

methods) we are in a position to make some initial remarks

concerning the magnitude and anisotropy of the thermal

expansion and the behaviour of the material on warming

above 273 K. A more detailed experimental study of these

phenomena is planned. Table 10 gives the unit-cell parameters

at 10 and 100 K determined from the single-crystal neutron

experiment, and at 245 K as determined by powder X-ray

diffraction.

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Acta Cryst. (2014). B70, 948–962 A. Dominic Fortes et al. � Structure of ammonium carbonate monohydrate 959

Figure 12Comparison between the ammonium symmetric and asymmetric bending regions of the spectrum (cf. Fig. 11) and their associated bands due tocombination with the librational mode. The upper sets of data have been red-shifted equally by 500 cm�1. The carbonate stretching modes in (a) arecoloured grey for clarity.

Figure 11Deconvolution of the mid-frequency bands and interpretation in terms of the normal modes responsible. Individual pure Lorentzian contributions aredrawn in red whilst the sum is drawn in blue. Band centres and 1� uncertainties are obtained by least-squares fitting. The scatterplots underneath thespectra report the residuals between the best fit and the data.

These data are illustrated in Fig. 13, which includes a

qualitative representation of the anisotropic thermal expan-

sion in the form of dashed lines, effectively no more than a

visual guide. Both the a-axis and the b-axis of the crystal

expand normally on warming (although the b-axis may exhibit

a small amount of negative expansion below 100 K), whereas

the c-axis contracts. Estimates of the thermal expansivities

along the three orthogonal directions at 245 K are �a = �b ’

80 � 10�6 K�1 and �c’ �1 � 10�6 K�1, resulting in a volume

thermal expansion of approximately 160 � 10�6 K�1. In other

words, upon warming the crystal experiences the greatest

expansion parallel to the chains drawn in Fig. 5 whilst

undergoing a small degree of contraction perpendicular to

those chains. The volume coefficient of thermal expansion is

similar to that of water ice Ih at the same temperature

(Rottger et al., 1994).

X-ray powder diffraction data reveal that ammonium

carbonate monohydrate begins to transform to ammonium

sesquicarbonate monohydrate at around 273 K; this transfor-

mation is complete in under an hour at 291 K. After being left

in air at 299 K for 2 h, we found that crushed single crystals of

ammonium carbonate monohydrate had transformed

completely to ammonium bicarbonate.

4. Summary

We have determined the crystal structure of ammonium

carbonate monohydrate, a substance that we find to be stable

in air only at temperatures below 273 K, explaining why this

otherwise ubiquitous laboratory reagent has been consistently

misidentified over the decades. Unlike the related sesqui-

carbonate and bicarbonate of ammonia, the ‘normal’ carbo-

nate consists of co-planar chains of strongly hydrogen-bonded

NH4+ and CO3

2�. This moderately strong hydrogen bonding

results in a barrier to free rotation of the ammonium ion

second only to ammonium fluoride. The structural archi-

tecture is manifested in highly anisotropic linear thermal

expansion coefficients, including a negative expansivity along

the c-axis of the crystal. Undoubtedly the material will exhibit

a large elastic anisotropy, like the similarly layered ammonium

oxalate monohydrate (Kuppers, 1972) and we predict that the

a-axis will prove to be the most compressible direction in the

crystal whilst the c-axis will be the least compressible.

The authors thank the STFC ISIS facility for beamtime, and

thank ISIS Technical Support staff for their invaluable assis-

tance. We thank Lauren Milne for assistance with the photo-

graphy of the grown crystals and collection of some Raman

spectra. ADF acknowledges financial support from the UK

Science and Technology Facilities Council (STFC), grant

numbers PP/E006515/1 and ST/K000934/1, and from Birkbeck

Department of Earth and Planetary Sciences for the purchase

of our Raman spectrometer. ERH acknowledges support from

the Spanish Research and Innovation Office through project

No. FIS2012-31713.

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